Building societies are attracting 63 per cent of the new money coming into Tessa accounts.
The societies suggest that this shows that will be a competitive force in when the ISA market launches next April.
Latest figures from the Bank of England reveal that although building societies account for just 30 per cent of outstanding Tessa balances, consumers are increasingly turning to them to house their tax free savings.
Building Societies Association director-general Adrian Coles says: "This is further evidence that consumers are recognising building societies' competitive edge. Customers are increasingly turning to building societies for the attractive rates of interest and as a safe home for their tax free savings."